Fig. 4.  Poincaré analyses revealed differences in rapid eye movement (REM) sleep duration as a function of aerobic capacity. (A  and B ) Each point represents the duration in seconds of one REM sleep episode (y-axis REMⁱ) relative to the duration in seconds of the previous episode of REM sleep (x-axis REMⁱ−¹). These plots summarize 463 REM sleep episodes for high aerobic capacity rats (HCR) and 450 REM sleep episodes for low aerobic capacity (LCR) rats. (A ) illustrates key features used to interpret the Poincaré plot. Short-term variability (SD1) is the SD for the dispersion of points relative to the line of identity (x = y). Short-term variability characterizes the variability in REM sleep duration from one REM sleep episode to the next. The centroid indicates the average duration of REM sleep episodes and is indicated at the point where the perpendicular line intersects the line of identity. The dispersion of points orthogonally to the line of identity was not significantly different in A and B, indicating no significant difference in short-term variability between HCR and LCR strains. Long-term variability (SD2) represents the dispersion of data points relative to the line passing through the centroid. Long-term variability conveys the variability in REM sleep duration as a result of aerobic capacity. The color codes at right indicate a larger number of overlapping data points in B than in A. (C ) Quantitative comparison of long-term variability revealed that low aerobic capacity rats had significantly more long-term variability in REM sleep duration than HCR rats. Thus, REM sleep was initiated more often by LCR rats than HCR rats and could not be maintained by LCR rats. Asterisk indicates a statistically significant difference between HCR and LCR rats.